Question

1/3-2/15+3/35-4/63+5/99-6/143=?分数简便计算

Answer 1

1/3-2/15+3/35-4/63+5/99-6/143

=[1/3-2/(3×5)]+[3/(5×7)-4/(7×9)]+[5/(9×11)-6/(11×13)]

=1/3×（1-2/5）+1/7×（3/5-4/9）+1/11×（5/9-6/13）

=1/3×3/5+1/7×7/45+1/11×11/117

=1/5+1/45+1/117

=2/9+1/117

=1/9×(2+1/13)

=1/9×27/13

=3/13